The split common fixed point problem of two infinite families of demicontractive mappings and the split common null point problem

Abstract

In this paper we introduce a new algorithm based on the viscosity iteration method for solving the split common fixed point problem of two infinite families of k-demicontractive mappings. We shall also study the split common null point problem, and the split equilibrium problem for this class of mappings. As an application, we obtain strong convergence theorems for the split monotone variational inclusion problem and the split variational inequality problem. Our results improve and extend the recent results of Cui and Wang [9], Takahashi [21], Tang and Lui [22], Moudafi [15], Eslamian and Vahidi [17], and many others.

A hybrid projective method for solving system of equilibrium problems with demicontractive mappings applicable in image restoration problems

“…Inspired and motivated by above works and the work of other studies 10,11,17,19,[29][30][31] in this paper, we modify CQ methods for finding a common solution set of system found in equilibrium problem and the fixed-point set of a finite family of demicontractive mappings. Further, we prove a strong convergence theorem for the sequences generated by iterative method and derive some consequences which are new and interesting.…”

Strong convergence of an inertial extrapolation method for a split system of minimization problems

“…The SFP and MSSFP arise in many fields in the real world, and numerous methods have been proposed to solve the SFP, see for example [3][4][5] and references therein, and MSSFP, see for example [6][7][8] and references therein. Moreover, there are some studies of fixed point problems in the framework of the MSSFP, see for example [9][10][11][12][13][14].…”